Finite Group Databasebeta

← C2×#13078788 #15621922

Subgroups — C2×#13078788 #15621922

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic
2C22×Q8×Dic11C211yesmaximal, characteristic, complemented
3#13078788C2116yesmaximal, direct product factor
4C2×#10622657C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic
6C2×#10622412C212yesmaximal, complemented
7C2×#10622798C212yesmaximal, complemented
8C2×#10622840C211yesmaximal, characteristic
9C2×#10622797C212yesmaximal, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#451C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×C11×Q16C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×#67000C2211yescharacteristic
17C2×Q8×Dic11—21no—
18C2×Q8×Dic11—21no—
19C2×Q8×Dic11—24no—
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2212yes—
22C2×Q8×Dic11C2212yes—
23C2×Q8×Dic11C2218yescomplemented
24C22×#4325C2212yes—
25C2×#66983C2211yescharacteristic
26C22×C4⋊Dic11—21no—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4×Dic11—21no—
29C22×C4×Dic11C2211yescharacteristic
30#10623155—24no—
31#10623155C2218yes—
32C2×#66951—21no—
33C2×#66946C2211yescharacteristic
34C2×#66945—21no—
35C2×#66943C2211yescharacteristic
36C2×#66939—21no—
37C2×(C22⋊D11)⋊C4—21no—
38C11×#451C2218yescomplemented
39C2×C11×#103C2212yes—
40C2×C11×C22⋊C8C2211yescharacteristic
41#10622840C2218yes—
42C2×#66899C2212yes—
43C2×#66899C2212yes—
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622798C22116yescomplemented
46#10622797C22116yescomplemented
47C2×#66885C2212yes—
48C2×#66881C2212yes—
49C2×#66879C2212yes—
50C2×Dic11⋊C8C2212yes—
51#10622657C2218yescomplemented
52C2×#66871C2212yes—
53#10622430C22116yescomplemented
54#10622412C22116yescomplemented
55#10622348C2218yes—
56#10622332C2218yescomplemented
57C22×Q8×C11—28no—
58C22×Q8×C11—21no—
59C22×Q8×C11—22no—
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2314yes—
62C22×Q8×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C23×Dic11D411yescharacteristic
68C23×Dic11D411yescharacteristic
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C2×C11×Q16—28no—
72C2×C11×Q16C2318yes—
73C22×C8×C11C2312yes—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79#67000—22no—
80#67000C2314yes—
81Q8×Dic11—24no—
82Q8×Dic11—24no—
83Q8×Dic11—28no—
84Q8×Dic11—28no—
85Q8×Dic11—22no—
86Q8×Dic11C2314yes—
87Q8×Dic11C2318yes—
88Q8×Dic11C2318yes—
89C2×#4325—28no—
90C2×#4325C2318yes—
91#66983—22no—
92#66983C2314yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—28no—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—28no—
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11D414yes—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2314yes—
118C22×C11⋊C8C2312yes—
119#66951—28no—
120#66946—22no—
121#66946C2314yes—
122#66945—28no—
123#66943—22no—
124#66943C2314yes—
125#66939—28no—
126(C22⋊D11)⋊C4—28no—
127C11×#103C2318yes—
128C11×C22⋊C8C2314yes—
129#66899C2318yes—
130#66899C2318yes—
131C22⋊(C11⋊C8)C2314yes—
132#66885C2318yes—
133#66881C2318yes—
134#66879C2318yes—
135Dic11⋊C8C2318yes—
136#66871C2318yes—
137C2×#3117—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×Q8×C11—216no—
141C2×Q8×C11—28no—
142C2×Q8×C11—216no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—21no—
146C2×Q8×C11—24no—
147C2×Q8×C11—24no—
148C2×Q8×C11#4118yes—
149C2×Q8×C11C2412yes—
150C2×Q8×C11C2414yes—
151C22×C4×C11—28no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—44no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—44no—
169C22×Dic11C2×D414yes—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D414yes—
175C2×D44—21no—
176C2×D44—24no—
177C2×D44C2412yes—
178C2×C4×D11—24no—
179C2×C4×D11—44no—
180C11×Q16—216no—
181C2×C8×C11—24no—
182C2×C8×C11C2414yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4C2412yes—
186C11×C22⋊C4—24no—
187#4325—216no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11—28no—
195C4⋊Dic11—28no—
196C4⋊Dic11—21no—
197C4⋊Dic11—24no—
198C4⋊Dic11—22no—
199C4⋊Dic11C2414yes—
200C4⋊Dic11C2412yes—
201Dic11⋊C4—24no—
202C4×Dic11—24no—
203C4×Dic11—28no—
204C4×Dic11—28no—
205C4×Dic11C2×D412yes—
206C4×Dic11C2×D414yes—
207C4×Dic11C2×D412yes—
208C4×Dic11C2×D414yes—
209C4×Dic11C2412yes—
210C4×Dic11C2412yes—
211C2×C11⋊C8—24no—
212C2×C11⋊C8C2414yes—
213C2×#529—111no—
214C22×C4×Q8—111no—
215#3117—1116no—
216C2×#484—111no—
217C2×#481—111no—
218C2×#479—112no—
219C2×#464—112no—
220C2×#451D1111yescharacteristic, complemented
221C2×#448—111no—
222C2×#441—112no—
223C2×#440—112no—
224C2×#432—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11#13714yes—
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234Q8×C11—216no—
235Q8×C11—28no—
236Q8×C11—24no—
237Q8×C11—24no—
238Q8×C11—42no—
239Q8×C11C2×#4118yes—
240C2×C4×C11—216no—
241C2×C4×C11—28no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4114yes—
253C2×C4×C11C2511yescharacteristic
254C22⋊D11—48no—
255C2×Dic11—28no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—44no—
263C2×Dic11—48no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268C2×Dic11C22×D412yes—
269C2×Dic11C22×D412yes—
270D44—24no—
271D44—42no—
272C4×D11—48no—
273C8×C11—24no—
274C11⋊C8—24no—
275C23×Q8C2×D1111yescharacteristic
276C22×Q16C2×D1112yes—
277C22×SD16—112no—
278#529—118no—
279#529—224no—
280C2×#126—221no—
281C2×#125—111no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8C2×D1111yescharacteristic
285C2×#121—111no—
286C2×C4×Q8—112no—
287C2×C4×Q8—118no—
288C2×C4×Q8—112no—
289C2×C4×Q8—111no—
290C2×C4×Q8—221no—
291C2×C4×Q8—221no—
292C2×C4×Q8—224no—
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×#117—221no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—221no—
298C22×C42—111no—
299C22×C42—221no—
300#484—118no—
301#481—118no—
302#479—1116no—
303#464—1116no—
304#451C2×D1118yescomplemented
305#448—118no—
306#441—1116no—
307#440—1116no—
308#432—118no—
309C2×#107—112no—
310C2×#106—112no—
311C2×C4⋊C8—112no—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103C2×D1112yes—
315C2×#102—112no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11#52512yes—
323C22×C11C2×#13714yes—
324C22×C11C2×#13712yes—
325C22×C11#57512yes—
326C22×C11C23×D411yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—84no—
331C4×C11—28no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11#52512yes—
336C4×C11C22×#4112yes—
337Dic11—22no—
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—42no—
342Dic11—44no—
343C22×Q8—28no—
344C22×Q8—22no—
345C22×Q8—21no—
346C22×Q8C22×D1114yes—
347C22×Q8C22×D1111yescharacteristic
348C22×Q8C22×D1112yes—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—21no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357C2×Q16—28no—
358C2×Q16C22×D1118yes—
359C2×SD16—118no—
360C2×SD16—228no—
361C22×C8—112no—
362C22×C8C22×D1112yes—
363#126—228no—
364#125—114no—
365#125—222no—
366#124—114no—
367#124—222no—
368#123—228no—
369C22⋊Q8—22no—
370C22⋊Q8C22×D1114yes—
371#121—114no—
372#121—222no—
373C4×Q8—118no—
374C4×Q8—118no—
375C4×Q8—114no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×Q8—224no—
379C4×Q8—228no—
380C4×Q8—222no—
381C4×D4—114no—
382C4×D4—222no—
383C4×D4—228no—
384#117—228no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—228no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—114no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—114no—
409C2×C42—221no—
410C2×C42—228no—
411C2×C42—222no—
412C2×C42—222no—
413#107—118no—
414#106—118no—
415C4⋊C8—118no—
416#103—118no—
417#103—118no—
418#103C22×D1118yes—
419#102—118no—
420C22⋊C8—114no—
421C22⋊C8C22×D1114yes—
422#97—118no—
423C2×C11—24no—
424C2×C11#311714yescomplemented
425C2×C11C2×#52511yescharacteristic
426C2×C11C22×#13711yescharacteristic
427C2×C11C2×#57511yescharacteristic
428D11—82no—
429C24—221no—
430C24D4×D1111yescharacteristic
431C2×Q8—216no—
432C2×Q8—28no—
433C2×Q8—216no—
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8#434118yes—
440C2×Q8C23×D1112yes—
441C2×Q8C23×D1114yes—
442C2×D4—112no—
443C2×D4—224no—
444C2×D4—221no—
445C2×D4—224no—
446C2×D4—444no—
447C22×C4—28no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—114no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—114no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—444no—
465C22×C4—442no—
466C22×C4—444no—
467C22×C4D4×D1112yes—
468C22×C4D4×D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—216no—
472SD16—2216no—
473C2×C8—24no—
474C2×C8—114no—
475C2×C8—224no—
476C2×C8C23×D1114yes—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—114no—
480C4⋊C4—112no—
481C4⋊C4—228no—
482C4⋊C4—228no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—222no—
488C4⋊C4—221no—
489C4⋊C4C23×D1112yes—
490C22⋊C4—24no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C42—114no—
496C42—112no—
497C42—112no—
498C42—114no—
499C42—112no—
500C42—112no—
501C42—228no—
502C42—228no—
503C42—224no—
504C11C2×#311711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—222no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23#6697114yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1111yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—24no—
518Q8—42no—
519Q8C2×#434118yes—
520D4—224no—
521D4—448no—
522D4—442no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—228no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—448no—
545C2×C4—444no—
546C2×C4—448no—
547C2×C4—442no—
548C2×C4—444no—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434114yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—224no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062311712yes—
563C22C2×#6697114yes—
564C22C2×#6697112yes—
565C22#1062330812yes—
566C22C22×D4×D1111yescharacteristic
567C4—28no—
568C4—22no—
569C4—42no—
570C4—42no—
571C4—222no—
572C4—222no—
573C4—222no—
574C4—222no—
575C4—442no—
576C4—444no—
577C4#1062311712yes—
578C4C22×#434112yes—
579C2—24no—
580C2—882no—
581C2#1307878814yesdirect product factor
582C2C2×#1062311711yescharacteristic
583C2C22×#6697111yescharacteristic
584C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#451D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×Q8×Dic11C2semidirect
3. #13078788C2direct (N × H)
4. C2×#10622657C2semidirect
6. C2×#10622412C2semidirect
7. C2×#10622798C2semidirect
9. C2×#10622797C2semidirect
10. C2×#10622430C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#451C2semidirect
23. C2×Q8×Dic11C22semidirect
38. C11×#451C22semidirect
45. #10622798C22semidirect
46. #10622797C22semidirect
51. #10622657C22semidirect
53. #10622430C22semidirect
54. #10622412C22semidirect
56. #10622332C22semidirect
220. C2×#451D11semidirect
304. #451C2×D11semidirect
424. C2×C11#3117semidirect
504. C11C2×#3117semidirect
581. C2#13078788direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106231552
C22×Q8×Dic112
#130787882
C2×#106226572
C2×#106223482
C2×#106224122
C2×#106227982
C2×#106228402
C2×#106227972
C2×#106224302
C2×#106223322
C2×C11×#4512
C2×#311711